TER VERKRIJGING VAN DEN GRAAD VAN
DOCTOR IN DE WIS- EN NATUURKUNDE
AAN DE RITKSUNIVERSITEIT TE UTRECHT, OP
GEZAG VAN DEN RECTOR MAGNIFICUS
DR. H. BOLKESTEIN, HOOGLEERAAR IN DE
FACULTEIT DER LETTEREN EN WIJSBE-
GEERTE, VOLGENS BESLUIT VAN DEN SENAAT
DER UNIVERSITEIT TEGEN DE BEDENKINGEN
VAN DE FACULTEIT DER WIS- EN NATUUR-
KUNDE TE VERDEDIGEN OP DINSDAG
9 JULI 1935, DES NAMIDDAGS TE 3 UUR

Bij het beëindigen van dit proefschrift betuig ik mijn oprechte
dank, aan allen, die tot mijn wetenschappelijke vorming hebben
bijgedragen.

In het bijzonder is het mij een behoefte U, Hooggeleerde
Ornstein, Hooggeachte Promotor, dank te brengen voor de leiding
en levendige belangstelling, die ik zoowel bij de onderzoekingen
voor dit proefschrift, als bij andere onderzoekingen van U heb
mogen ondervinden. Dat ik onder Uw leiding in aanraking ben
gekomen met problemen behoorend tot het gebied der toegepaste
wetenschappen, acht ik een groot voorrecht.

U zult wel willen gelooven, dat de belangstelling, die ik naast
mijn laboratoriumwerk van U mocht ondervinden, voor mij van

Truus Eymers, ik ben je dankbaar voor onze langdurige samen-
werking, waarin wij aan vele problemen werken mochten. Dat ik
als onderwerp voor een proefschrift één onzer problemen kiezen
mocht, waarbij ik mijn neiging tot precisie metingen volgen kon,
dank ik aan jouw vriendschappelijke welwillendheid.

CHAPTER I. Determination o£ the relative spectral distribution
o£ energy according to the monochromator method

In a report, issued by the Dutch Committee for photometry for
the I. C. I. (1931) a method was described for measuring spectral
intensities, on which the definition of the light unit can be based ( 1 ).
For reasons of principle, defining the light unit with the aid of a
method, by which the spectral energy distribution can be determined
in an absolute measure, is to be preferred to fixing it by means of
a standardized light source as e.g. the black body. For, as a general
rule, one must, in fixing units, define the unit in question, if at
all possible, by means of already established standard values. In
the case of the light unit, this can be done by choosing as a unit
the flow of energy characterised by a definite number of erg/sec,
and a spectral distribution, both of which are to be agreed upon
by general consent.

During the discussions at Cambridge in 1931 concerning the
light unit stress was laid on the condition that only when the
measuring method for objective spectral photometry should have
reached an accuracy of 0,1 %, the spectral energy distribution
could serve as a basis for the definition of that unit.

On account of this condition, investigations have been carried
out in the Utrecht laboratory, with a view to increasing the
accuracy.

The problem involved, has been treated in two parts, firstly the
relative measuring in the spectrum has been worked out to the
highest possible degree of accuracy, and secondly the precision
of an absolute energy measurement has been investigated.

The present thesis deals with the former part, for the latter part,
the reader is referred to the thesis written by J. wouda.

In the first chapter the measuring method is described in detail.
In the second chapter the method is applied to the determination
of the relative energy distribution in black radiation at the melting
temperature of gold, from which as a further result the value of
Planck's constant c2 is deduced.

Determination of the relative spectral distribution of energy
according to the monochromator method.

In a paper on the measurement of intensity ratios between
spectral lines at great distances from one another, L. S. Ornstein
has shown the principle of the method of measuring which we shall
explain by means of a schematic figure (fig. 1) of the arrangement
(2, 3).

With an auxiliary lamp Q, a tungsten band lamp, and a mono-
chromator M, images of a definite colour are obtained of the back-

slit of the latter instrument in P. The proportions of the energy in
the coloured images in P are measured by a non-selective radiation-
receiver. Once these proportions known, the images play the part
of a primary standard source of light with which a lamp to be
standardized is compared for various wave-lengths by means of
a spectral apparatus Sp. To this end the proportions of the intensity
in the image P and the source of light to be standardized placed
also at P are measured for various wave-lengths.

This must be carried out in such a way that the percentage of
energy lost by the light on its way from P to the receiver behind
the spectral apparatus is the same for the coloured images and
for the lamp to be standardized for each wave-length, since in that
case only, the measured intensity ratio will indeed be the true
intensity ratio. In order to meet these requirements the following
conditions must be borne in mind.

the hght when it is illuminated by the images P and by the lamp
to be standardized must be identical.

2. The light emerging from the monochromator is partly
polarized. The ordinary light from the lamp to be standardized
is thus compared with the polarized light of the images P, which
may give rise to errors, owing to the fact that the power of trans-
mission of the spectral apparatus for various wave-lengths is
dependent on the polarization of the light falling upon it.

The following contrivance suggested by W. J. D. van DycK
enables us to satisfy both these conditions at the same time. Images
are formed of the images at P and of the lamp to be standardized
on a diffusely reflecting white surface W (magnesium oxide) which,
as a secondary light source, radiates on to the spectral apparatus.
The polarized light is thus depolarized by the diffuse reflection;
the light therefore, which the images at P as well as the lamp
cast on to the apparatus is ordinary light which, moreover, traverses
the instrument in both cases along the same paths.

We want to measure the relative spectral distribution of the lamp
to be standardized, that is, the intensity, measured in an arbitrary
unit, radiated per spectral region of 1 A, as a function of the
wave-length. It is, therefore, necessary to find out the energy of
the images per A. The relative energy per A of the images P is
found from the energies measured and from the knowledge of the
wave-length regions let through.

From the above it is seen that a determination of the spectral
distribution of energy in light sources requires the three following
measurements:

c.nbsp;,,nbsp;„nbsp;„ ,, ratio of intensity in the images P
and the lamp to be standardized, at various wave-lengths.

In the following paragraphs we give first a brief description of
the arrangement used, followed by a detailed description of the
methods of measuring and the apparatus employed, in which we
discuss as well the various sources of errors. The accuracy with
which a spectral energy-measurement can be carried out is discussed
in the last paragraph.

A tungsten bandlamp provided with a vertical band, serves as
the auxiliary lamp in fig. 1. A compensating arrangement is used
for the accurate testing whether the strength of the electric current
is constant. It is further necessary to ascertain whether the radiation
is constant for constant current. The measurements carried out to
this purpose are described in § 7.

For these experiments a double monochromator, after van
Cittert (4) has been used. A bolometer has been selected as a
radiation receiver. An image of the back slit of the monochromator
is formed, by means of a combination of two Zeiss Tessar lenses L2
on to a horizontal bolometer strip of the vacuum bolometer placed
at P. In this way we measured the energy with small slit-height.
This offers advantages as regards the curvature of the images of
the front-slit ; reference will be made to this point in further detail
in the description of the double monochromator (§ 7).

For measuring the wave-length regions (§ 4) an image of the
back slit is formed by a rectangular prism and a microscope objective
aa on the slit of a Hilger spectroscope placed perpendicularly to
the path of light behind the monochromator. As light sources, of
which the spectral distribution of energy is measured, we chose
tungsten band lamps. In order to get the band exactly in point P
(the place of the illuminated bolometer-strip) we used a telescope
with cross-wires, placed as perpendicularly as possible to the
direction of the light-path behind the monochromator. The light
reflected by the bolometer-strip is just sufficient to focus the
telescope accurately on P. The band-lamp to be standardized is
mounted on a stand which allows of small displacements in three
mutually perpendicular directions. By lens L^ an image of the
image P, respectively of the band-lamp, is formed on the white
surface.

Since the comparison between the spectral distribution of the
energy of the lamp, to be standardized, and of the images P, is
made via a white surface, it is necessary to measure weak intensities.
The photographic, photo-electric and the spectral-pyrometric
methods, can, therefore, be applied. In our measurements we made
use of the last mentioned method.

In our measurements we must concern ourselves with the total
energy-current in the direction of the width of the images. For the
energy per surface-unit in different parts of the image of the
back-slit is not constant but diminishes towards the smaller wave-
lengths. The radiation receiver, therefore, must collect the radiation
of the whole image in its full breadth, and be of a homogeneous
sensitivity in that direction. A bolometer, of which the strip is
placed perpendicular to the images, meets with this requirement.
We made use of a vacuum-bolometer provided with two bolometer-
strips. (See description of bolometer in § 7).

Two kinds of disturbances occur in the use of the bolometer,
those, namely, due to changeable fields and to sudden extraneous
temperature changes. The same disturbances occur with thermo-
elements. In this respect the vacuum-bolometer with two strips has
a decided advantage over the thermo-element, for both kinds of
disturbances can be compensated by its construction and by its
electrical connecting system.

The changes in the resistance, caused by the radiation on to one
of the strips, is measured in a Wheatstone bridge. The electrical
arrangement is shown in fig. 2. The heating-current is supplied by
an accumulator which is regulated by a resistance-controller
Wj. The constancy of the current is checked by a compensating
arrangement. C^ and C2 are constant resistances of about 60 Ohm ;
they are two arms of the connecting-system of the bridge, while

the bolometer-strips Bi and 82 are the two others. The relay-galva-
nometer of Moll and Burger is used as reading instrument (5).

A rectifier cell of which the sensitive layer is divided into two
parts by a scratch, and which is arranged as indicated in fig. 3

acts as relay. The deviation of the primary galvanometer is increased
to such an extent that the disturbances due to Brownian movement
amount to about 0.2 mm, which corresponds to an E. M. F. in the
primary galvanometer circuit of 5 X 10—lo volt.

The changes in the resistance dW arising from the exposure of
one of the strips to the radiation causes a difference of potential
idW between the points P and Q. This difference is compensated
by applying a E. M. F. between A and B. In order to take into
account a slow change of zero we proceeded as follows :

The resistance W2 (precision rheostat) is chosen in such a way
that the potential difference between P and Q is almost compensated
and is subsequently changed by successive steps until a deflection
of the opposite sign is obtained. The deflections are registered while

after every 3 or 4 deflections zero
is registered. A registrogram is
thus obtained which is schemati-
cally shown in fig. 4. It will be
clear that a slight change in zero
can be brought into account by
tracing a dotted line through the
registered zeros. In order to
increase the accuracy of our
measurings we have photogra-
phed on the registrogram, with the drum at rest, equidistant lines
of reference, which indicate the direction of the deflection. When
measuring the deflections the measuring-rule is held parallel to the
line of reference. Particularly in the case of considerable changes
in zero the accuracy of the measuring is greatly increased by the
use of these lines of reference, as without them there would be a
decided tendency to put the measuring-rule perpendicular to the
zero-line.

In order to eliminate the effects of fluctuations in the auxiliary-
lamp Q (fig. 1) during our investigation of the properties and the
accuracy of our arrangement, we have included a constant and
reproducible E. M. F. in the circuit PABQ of fig. 2 (cp. fig. 5).

The resistance is varied in steps in such a way that we obtain a
deflection to the right and to the left of zero. The relay is adjusted
in such a way that during dead current the secondary galvanometer,
too, reads zero. We found that for deflections up to 4 cm to the
right and left of zero the reading is linear. Furthermore, we have
investigated whether the sensitivity is dependent on the changes
of zero. To this end the sensitivity was measured for the case that
with the contactors S^ and S2 open, the secondary galvanometer
too is deflected relatively to its own zero. (This means, therefore,
that the image reflected by the mirror of the primary galvanometer
falls asymmetrical with relation to the scratch on the rectifier-ceU).
It then appeared that the sensitivity is not dependent on the asym-
metrical position of the image relatively to the scratch, so long as
the degree of asymmetry corresponds to deflections of the secondary
galvanometer smaller than 1.5 cm 1).

In order to investigate the accuracy of measuring we made our
registrations with a constant resistance of 10500 Ohm at a and a

resistance in b, which starting from 11000 Ohm, was diminished
in steps of 100 Ohm down to 10400 Ohm, while after every 3 or 4

deflections zero was registered. We repeated this registration
7 times. From each of them we obtained the E. M. F. which com-
pensates the voltage supplied by AaB (fig. 5). From these values

we calculated the mean error of a single observation ]/for
which we found 0,4 %.

In order to deduce the energy per A from the measured energy
of an image P, it is necessary to know the spectral region let
through, that has contributed to it: more precisely, the trans-
mission curve for the wave-length adjustment of the monochro-
mator associated with that region. We understand by quot;trans-
missionquot; for a spectral line with a given adjustment of the
monochromator, the ratio between the energy let through with that
adjustment, and the energy let through when the adjustment of
the monochromator corresponds exactly to the wave-length of the
line.

The transmission-curve can be determined by means of a direct
experimental method, viz. the method of crossed prisms, or, it can
be calculated from the dispersion-curve. For various reasons which
we shall mention at the end of this paragraph we chose the first
method, using a line light source.

An enlarged image of the back-slit of the monochromator M
is formed by means of an aa-microscope object-glass on the slit,
of a Hilger spectroscope. The latter instrument is mounted in such
a way that the axis of the eye-piece is vertical. By this arrangement
the slit of the spectroscope and the image of the back-slit are
mutually perpendicular. The images of the back-slit jaws run
parallel to the direction of dispersion, in the field of the spectros-
cope. The latter is provided with a micrometer eye-piece.

Let us now observe what is shown in the spectroscope when
the front-slit of the monochromator is illuminated by a line light

source. A number of monochromatic images of this front-sht is
formed in the plane of the back-slit. We adjusted the monochro-
mator, in such a way, that a monochromatic image of the front-slit
coincides exactly with the back-slit. In this case one observes in

the spectroscope a small rectangle
of which the edges, parallel to the
direction of dispersion, are the images
of the right and left jaw of the back-
slit of the monochromator (See fig. 6
type b). The width of the rectangle
is determined by the slit-width of the
spectroscope. The wave-length ad-
justment of the monochromator may
be such, however, that the back-slit
is not quite filled and part of the monochromatic image is cut off
by the left jaw. In the spectroscope one sees then a rectangle, type
a, as in fig. 6, whereas monochromatic images cut off by the right
jaw are rectangles of type c. When the front-slit of the mono-
chromator is illuminated by a light-source in which many lines
lie close together the spectroscope shows all three types described
at the same time.

From our definition of transmission it will be clear that with a
given reading of the wave-length index of the monochromator, the
transmission is equal to the ratio between the actual height of the
rectangle and the maximum height that can be obtained by moving
the wave-length index. When the adjustment is such that the
spectroscope shows two small rectangles of type a and b, (fig. 6),
the transmission for the spectral line a for that adjustment will

Now, the transmission-curve is found from the heights, measured
with the eye-piece micrometer of the various monochromatic
rectangles arising from the illumination with a line hght-source.

The measuring of the heights of the various spectrum-lines is,
however, tedious and takes a long time ; by the following device
it can be considerably shortened. An object micrometer with
divisions of 0,1 mm is attached to the slit of the spectroscope.

In the latter instrument one sees then, dark lines corresponding to
the scale divisions at right angles to the spectrum-lines (fig. 7).
Adjustment for longer wave-lengths will lengthen the spectrum-

lines 5, 6 and 7 and shorten the lines 1,2,3 and 4; now, one can
adjust to a high degree of precision the wave-length index so that
either the upper or the lower edge of a spectrum-line coincides
exactly with one of the scale divisions of the object micro-
meter, or that a line is on the point of appearing at A^ or of
disappearing at Bo, or that the end of a line just touches b in B
or begins to shorten at A2. We can find the connection between
the position of the wave-length index and the true wave-length

A2P2Q2P2S2B2gt; taking care to
turn the screw in the same direc-
tion all the time to avoid back-
lash. Curves, showing this con-
nection are given in fig. 8. The
distances between the divisions
p and s and the edges of the
images of the back-sht jaws, i.e.
the distances bs and ap in fig. 7

For a given reading of the vi^ave-length index the transmission
as a function of the wave-length is then found from the curves
A^Pi etc. of fig. 8, by simply reading from them the value for A,
associated with this reading. For, the transmission for that wave-
length of the curve Qj^ is proportional to 0.5 mm ap.

back-sht, one can represent the transmission D;. approximately as
a function of the wave-length by two sides of a triangle. This

would be rigidly true if the second
D derivate of the dispersion-curve were
zero; as it is, one finds for D;. an
asymmetrical figure relatively to
when /io denotes the wave-length of
maximum transmission (see fig. 9a).
When the size of the front-slit image
is not the same as that of the back-
sht, the transmission as a function
of the wave-length can be repre-
sented approximately by three sides
of a trapezium (fig. 9b).

/	/^
—	C
B	= C

Fig 10.

prisms and continuous
light source.
Van Alphen (3) applied the
method of crossed prisms for mea-
suring the wave-length region while working with a continuous
light-source. In this case the spectroscope shows a parallelogram

(fig. 1 Oa). It will be clear that the wave-lengths A, B.C and D in that
figure are the same as those denoted by the same letters in fig. 10.

The measuring of the wave-length at the vertices of the parallelo-
gram must be done by means of reading the drumhead of the
Hilger-spectroscope; the highest accuracy obtainable by these
readings is 1 Ä. This means that for a region of 100 Ä the precision
is at most 1 % to 2 %. One could perhaps obtain a higher precision
photographically.

A very usual method of determining the transmission-curves for
various wave-length adjustments of the instrument is from the
dispersion-curve and the known slit-width. This is done as follows:
For a certain wave-length adjustment Xq of the monochromator,
the monochromatic image of the front-slit coincides exactly with
the back-slit for the wave-length -Iq- For this wave-length D;.,, is
put arbitrarily equal to 1. The points A and D of the transmission-
curves (see fig. 9) are formed by reading from the dispersion-curve
the wave-lengths at distances b to the right and left of Xq, equal
to the slit-width; the image of the front-slit and the back-slit are
here supposed to be of the same size. The shape of the transmission-
curve is then found by reading the wave-lengths to the right and
left of Xq at various distances y, where Dx is proportional to
b~y {ij^b). The precision attainable in the determination of Dx
is in this case dependent on the precision with which the width of
the back-slit and the width of the front-slit image can be measured.
By means of a comparator it is possible to measure a width of
0,5 mm with an error of 0,02 mm; now, assuming the error in
measuring the front-slit image to have the same value, the result
is that it is impossible to determine the wave-length region let
through with an error smaller than 1 or 2 %.

From a comparison of the three methods here described it will
be apparent that the method of crossed prisms with line light source
illumination offers various advantages, namely:

1. The shape of the transmission-curve as a function of the
wave-length can be determined wholly by experiment.

2.nbsp;The wave-lengths of the lines used can be looked up with
sufficient accuracy in the international tables.

4.nbsp;Index errors of the monochromator play no part. (By index
errors we understand, in the case of our double monochromator, the
differences between the readings of the wave-length index and the
true displacements of the intermediate-slit.)

For the spectral comparison of the intensities of the lamp to be
standardized with the images P (§ 6) it is necessary to know the
brightness per A of the images. To this end the energy of the
images is measured and also the transmission as a function of the
wave-length at the corresponding index readings. From these
measurements the brightness per A (in an arbitrary measure) is
obtained in the following way:

here /' and denote the limits of the wave-length region let through
for a definite adjustment of the monochromator, D), the transmission
as defined above, E), the energy pro unit of surface and pro A of
the image at P, h the width of the image and 5 the width of the
bolometer-strip.

When the size of the images P is independent of the wave-length
the indication of the bolometer is proportional to :

For a given adjustment the shape of the transmission-curve
can be represented with very good approximation by a trapezium
(fig. 4) i.e. expressed mathematically:

In the case of continuous light source illumination the energy
of the image jE^ is given by

where the reducing factor a is supposed to be independent of the
wave-length over the region /I4—

If we have equi-energy distribution in our continuous light-source,
we can write:

In this case the energy per A in the images is equal to the
measured energy divided by the wave-length region (a 6)
— This is what we shall call in future the quot;effectivequot; wave-
length region. For our energy measuring we used a continuous

light-source for illuminating the front-slit, namely, a tungsten band
lamp of which the distribution of energy can be described by a
colour temperature of 2800° K.

We have used formula (2) for computing the correction to be
applied when the energy per A is determined as the quotient of
the energy measured and the effective wave-length region. For
the computation of these corrections the values of the quantities
e] and e] introduced above, must be known for 2800° K. These
values computed with C2 — 1.432 X lOS (A degrees) are collected in
table 1 ; where the wave-lenght is given in A, the temperature
in degrees Kelvin.

We must mention here a complication, occurring when a double
monochromator is used. In this instrument an image of the front-
slit is formed on the intermediate slit and again an image of the
latter on the back-slit (§ 7). Now the widths of these three slits
may be combined either in such a way that the width of the mono-
chromatic images at the back-slit is larger or in such a way that it
is smaller than the width of the back-slit itself. We must inquire
therefore, how the widths of the various slits must be combined,
in order, to make an accurate determination of the brightness per A
of the images possible. Suppose the width of the back-slit to be
larger than that of the monochromatic images, the energy, incident
on the bolometer-strip is then given by:

where bx denotes the width of the images. With the aid of the
method of crossed prisms (§ 4), b)_ must then be measured as a
function of the wave-length, so that in computing the brightness
per A, one can take into account the change of bx with the wave-
length.

That this complication is not a superfluous refinement of the
computation, is proved by the fact that for our double monochro-
mator bl appeared to be indeed dependent on the wave-length.

It will be clear, however, that for the sake of accuracy, this
complication must be avoided.

It is advisable, therefore, to choose the widths of the three slits
in such a way that the width of the back-slit is smaller than the
monochromatic images in the plane of the latter.

§ 6. Spectral comparison of a lamp to be standardized with
the coloured images.

For the spectral comparison of a lamp to be standardized with
the images as explained in § 1 a white surface is essential. Owing
to diffuse reflection due to that surface we are limited to weak
intensities; the following three methods are, therefore, indicated:

In the region 4800 A—6800 A the intensity comparisons were
carried out with the aid of a spectral pyrometer. This involves the
visual adjustment on equal brightness, it can, therefore, not be
called an objective-method. In visual monochromatic photometry the
mean error of one measurement amounts to 1 % ; using the photo-
graphic method, taking every precaution, it amounts to 1 %. To
form an opinion of the precision of photo-electric intensity measure-
ments in the case of weak intensities (with which we are here
concerned) we have compared the sensitivity of the photo-electric
arrangement as described in the thesis of H. C. Hamaker (6), with
that of the spectral pyrometer. From this comparison it appeared
that by the photo-electric method one can attain in our case a
precision of 0.1

What induced us to choose the spectral pyrometric method rather
than the photographic and the photo-electric methods, was its great
simplicity.

If, however, one wishes to either work objectively or to cover
a greater spectral region, or to attain a higher precision, the photo-
electric method is, without doubt, the most suitable. In carrying
out the energy comparison of the lamp to be standardized with the

images, the following must be taken into account. The energy
per A at various wave-lengths of the coloured image on the diffuse
white surface is proportional to Eiq Dxm if Exq denotes the energy
per A of the auxiliary lamp Q in fig 1, and the spectral trans-
mission associated with a given adjustment of the monochromator.
Now, when the brightness is measured by means of the spectral
pyrometer and the latter is adjusted to the same wave-length Xq for
which the transmission of the monochromator is a maximum, we
have, for equal adjustment:

where ax„ denotes the reducing coefficient of the monochromator,
Exp the energy per A of the pyrometerlamp, Dxs the transmission
of the spectral apparatus of the pyrometer and Ox the sensitivity-
factor of the eye.

where Ey^Q for which we shall write denotes the energy
per A of the coloured image.

With the lamp to be standardized, radiating on to the white
surface, we have, on adjusting on equal brightness, the relation :

Ex^ denoting the energy per A of the lamp to be standardized.
Now, it follows from the method of standardizing of the spectral-
pyrometer that:

to know the transmission of the monochromator Dim as well as
the transmission Das of the spectral apparatus of the pyrometer at
the wave-length adjustments concerned. One can, however, avoid
the transmission-measurings of the latter instrument by making
the front-slit of the monochromator so widei) that the transmission
is the same for all wave-lengths in the region let through by the
spectral pyrometer. In this case the transmission curve of the
monochromator can be represented by three sides of a trapezium,
fig. 11, in which I2 — must at least be equal to the region let
through (fig. 12) by the spectral pyrometer. In formula 1 we
have then Dgt;,m= 1 and one finds for the various wave-lengths:

When a double monochromator after VAN CiTTERT is used we
can avail ourselves of the fact that by removing the intermediate
slit the emergent light is white, so that here the above-mentioned

condition which the wave-length regions, let through by the mono-
chromator and the spectral apparatus, must satisfy, no longer holds
good. Similar considerations apply to the photographic and the
photo-electric methods, only, the sensitivity-factor of the eye must

1) A wider back-slit would serve no purpose here, for one must remember
that the spectral-pyrometer measures surface brightness and that, therefore, the
monochromatic images on the white surface must coincide for the various wave-
lengths, for which C;.jvr=nbsp;occurs, in fact, when the front-slit is wider than
the back-slit.

Annealed tungsten band lamps with vertical band served as light-
sources. The hght of the auxiliary lamp Q (fig. 1) should remain
constant during the measurings ; the light of the lamp to be stan-
dardized should be constant and reproducible. The sources actually
employed by us were selected as follows. In the first place the
behaviour of the current was checked by means of a compensation-
connection. From this test it appeared that the electric-current of
various lamps was subject to irregular fluctuations. The second
test consisted in lightly tapping the bulbs of the lamps in order
to see if this had any effect. Those lamps whose electric current
showed irregularities and which were at all effected by the tapping
were excluded from the third test. The latter was concerned with
the constancy of the energy radiated at 6200 A. In order to find
this the radiated energy was measured every quarter of an hour for
three hours at a stretch, taking care to keep the strength of the
current accurately adjusted at the same value throughout. From
these measurements it appeared that in the course of a three hours'
running of the lamps the radiated energy had not changed. The
mean error of these measurements amounted to 0.5 %o- Finally
we investigated whether switching on again after dead current the
radiated energy attained the same value, measuring the energy
15 minutes after switching on. Here, too, the deviations did not
exceed the amount which can be reasonably expected from the
measuring errors.

We used the double monochromator after van cittert, which
consists of two similar monochromators A^j and M2 placed symme-
trically relatively to the place of the slit S2 (fig. 13). By moving
S2 in the plane of the image of Si one can make the various colours
emerge from the instrument. The movable slit S2 must be considered
as the front slit of the second monochromator which forms an image
of S2 in 53. Owing to scattering and reflection in the first monochro-

mator there will pass through S2 not only light of the spectral
region, determined by the slit width and the dispersion, but also
light of different wave-lengths, the so-called stray light. This
stray light, however, forms a spectrum in the plane of S3 and can,
therefore not emerge from the back-slit.

is the same as that of the mono-
chromatic image of in green.
The image which the second
monochromator forms of the
curved slit S2 on the slit S3 is
again straight and rectangular.
By this device, a greater light
intensity is obtained when a line
light source is used, and when a
continuous source is used it has
this advantage that the wave-
length region let through remains
the same along the height of the


N
	V
v'	lt;0	D
	—	S3

back-slit. We checked this for that part of the slit, which is focussed
on the bolometer strip.

The lenses A, B, C and D can be adjusted separately. By means
of a telescope focussed on infinity, A and C have been adjusted
once and for all at distances equal to their focal lenghts for yellow
from the slits Si and S2 respectively. The focussing of S^ on S2
and of S2 on S3 for the various wave-lengths is done by adjusting
the lenses B and D.

To examine the qualities of the monochromator we used the
same arrangement as for measuring the wave-length regions. The
spectroscope shows the back slit magnified about a hundred times.
The adjusting of the monochromator is accomplished as follows:

The front slit is illuminated by a line light source, for instance
a //e-vacuum tube and an image of the back-slit is thrown on to
the slit of the spectroscope by means of the microscope object glass;
whereupon the intermediate slit is made narrower than the third one.
By adjusting lens D, the slit S2 is focussed on S3 for the various
wave-lengths. From these adjustments it appeared that the lenses
of the monochromator were badly corrected both for spherical

as well as for chromatic aberration. The wavelength region let
through can only be accurately measured according to the method
described, when the images in the field of the spectroscope are
sharply defined. The van Cittert monochromator has lenses on
both sides of the intermediate slit. Since better images of the slits,
however, are obtained by removing these lenses, we carried out
our measurements without them, but the use of a diafragm remained
necessary. The size of the aperture of the diaphragm should be
such that sharp images are formed in the spectroscope and that
at the same time the light intensity is still sufficient for an accurate
energy measurement. A diaphragm of 1.5 cm diameter appeared
to meet both requirements. Finally, when an image of is formed
on Sg then, by adjusting B, an image of is formed on 52 after
the latter has been opened wide i).

A careful examination of the monochromatic images of the back-
slit in the spectroscope will reveal the existence of weak wings as

indicated in fig. 14 which must be
ri^hi jawnbsp;ascribed to scattered light of the double

—nbsp;monochromator. These wings show
particularly clearly whenever the wave-
length adjustment is such that a mono-
chromatic image of the back-slit is on
the point of appearing or of disappe-

as the quotient of the measured energy
Fig- 14.nbsp;and the effective wave-length region,

we investigated to what extent our
determination of the energy per A is affected by neglecting the

Owing to the chromatic aberration of the lenses, one must focus for each
spectral region separately. When high precision is required, one can therefore
not make use of the fact, that, on removing the intermediate slit, a white image
is formed in P, of which the spectral energy distribution is known. This property
of the double monochromator was applied by van Alphen. It has great
advantages when the lamp to be standardized is photographically compared with
the images. When, however, the photo-electric or the spectral-pyrometric method
is used, there is not the least objection to focussing for each spectral region
separately.

wing energy. To that end, we measured the ratio between the
brightness of the wing and of the rectangular image as follows :
an image of the back-slit of the double monochromator was
formed on the filament of a small standardized lamp (of which
the intensity as a function of the current strength is known) and
of this filament an image was formed on the slit of the hilger
spectroscope. The latter showed then the continuous spectrum of
the filament, at right angles to the monochromatic images of the
back-slit. The ratio between the brightnesses of the wings and of
the rectangles was then measured by us for the red and the yellow
He-line, taking care to measure the brightness of the wing as
closely as possible to the rectangle. In this way we found for the
intensity ratio 1 : 10^. In the green and blue regions this ratio is
more favorable.

For an effective wave-length region of a Ä, the energy of the
radiation incident on the bolometer-strip, when a continuous light
source is used for the illumination, is proportional to aEgt;., if the
energy contribution of the wing is neglected; Ei denoting the
energy per Ä of the auxiliary lamp.

Assuming the wing to cover one tenth of the back-slit width
with the same intensity as measured at the edge of the rectangular
image in the spectroscope, the energy contribution of the wing will
be proportional to a X 0.1 X 0.001 Ei. Owing to the wing, there-
fore, the result of the energy measurement will be 0.1 o/qq too high
so that our determination of the energy per Ä of the images, will
also give a value 0.1 ^loo too high.

After a few preliminary investigations we chose platinum as the
metal for the bolometer-strips. The blackening of the strips, when
the electrolytic method of lumivier and Kurlbaum is employed,
is largely dependent on the strength of the current applied. We
obtained a satisfactory blackening by using a current of 12 milli-
amperes during 4 minutes.

The energy-measurements were carried out with a bolometer,
provided with 2 Pt. strips, 1 jx thick and 0,5 mm wide.

The shape of the bulb must be such, that, once the instrument
is ready for use, the degree of blackness can be measured as often

as may prove advisable. To this end it should be possible, when the
incident hght is perpendicular to the strips, to measure the reflection
coefficient at various angles. This condition led to the construction
shown schematically in fig. 15.

To determine the degree of blackness of the bolometer-strips, we
compared the reflected energy with the incident energy by means
of the arrangement shown in fig. 161).

lens L. on the bolometer-strip B, which is placed perpendicularly to
the incident beam of hght.

The lamp, lens and bolometer can revolve together round the
centre of the strip. To measure the incident energy we put in B
a white surface (MgO), of which the intensity l(X, a), expressed

Owing to the construction of our bolometer, we could not employ the
method of measuring the power of reflection as worked out by HAMAKER. (6).

in an arbitrary measure, was determined at various wave-lengths as
a function of the angle. The influence of the glass window of the
bolometer was eliminated by placing a glass plate between L and B

in such a way, that the light
incident on the white surface,
passes through the glass but that
the intensity measurements are
made on reflected light which
has not passed through it. Fur-
thermore, we measured the ratio
between the brightness f{X, a) of
the strip and the white surface as
a function of a at various wave-
lengths ; this time the influence
of the glass window was
eliminated by placing a glass plate
immediately in front of the white surface. The total amount of
energy of a given wave-length, reflected by the white surface per
unit of area, is (fig. 17):

J


V ^ \ \ \ \ \ \ \ % \\ \ \ \ \	i » / / y i/ t/ Y

Fig. 17.

Assuming that the white surface does not absorb any energy at all
the power of reflection of the bolometer-strip is given by:

From measurements in the wave-length region from 5000 A to
6800 A it appeared that f(2, a) does not depend on X. The con-
struction of the bolometer and the way it was mounted permitted
us to carry out measurements over a range of a from 15° to 70°.
To investigate the behaviour of f(a) for a smaller than 15° we

have measured its value after placing the bolometer-strip at an
angle of 80° to the incident light. Its behaviour proved the same
as with perpendicular incidence. For small angles too, [{a) is
independent of 1.

As regards 7^(2. a), its values appeared to change at the various
wave-lengths in a way similar to a. Column 3 of table 2 shows
the behaviour of I^H a); the value of 1^(1 10°) is put arbitrarilv
equal to 100.

With the aid of the data given in table 2 we can compute the
total power of reflection of the bolometer-strip ; the result is 2,51 %.
Its power of absorption is therefore 97.49%. The white surface,
we assume here, does not absorb at all; this assumption can
influence only the absolute value of the power of reflection of the
bolometer-strip. The selectivity, of the power of absorption of MgO
in the spectral range considered, is not more than 1 %. This gives
for the selectivity of the power of absorption of the bolometer-strip
an error of 0.25 o/qq. The values given for [(a) and Iw{a) are
averages of six measurements, the mean error is smaller than 1 %.

From these measurements we can therefore conclude, with a
precision of at least 0.5 o/q^ that the power of absorption is
independent of the wave-length in the range from 5000 A to 6800 A.

The method described above of measuring the reflection of the
bolometer-strip can be applied to wave-lengths ranging from 4600 A
to 6800 A. For smaller wave-lengths one can use the photo-electric
method.

The sensitivity of the bolometer depends on the temperature of
the strips. To determine the sensitivity as a function of the heating-
current we used the arrangement shown in fig. 2, reading the
deflection of the galvanometer at various current strengths, while
one of the strips was exposed to constant radiation. From these
measurements (fig. 18) it appears that the sensitivity is a maximum
when the current strength is 100 m A. But on investigating the

behaviour of zero in the arrangement shown in fig. 2 this turned
out to be decidedly better when a current of 50 mA was used than
one of 100 m A. This must be ascribed to the fact that an accumu-
lator will stand the drain of a current of 50 mA with great con-
stancy for quite a long time, but not the drain of a current of
100 mA. Moreover, the precision of the measurements with a current
of 50 m A is higher than with one of 100 m A, notwithstanding the
smaller sensitivity. This was our reason for always using a current
strength of 50 mA for our energy-measurements.

We checked the proportionahty between the galvanometer deflec-
tions and the incident energy by varying the amount of energy
over a range from 1 to 100. To this end, images were formed on

the bolometer-strip, of a white surface of which the brightness was
altered in known ratios by variation of distance. The precision of
each measurement in this experiment did not exceed 0.5 %. The
deviations from direct proportionality are, therefore, of the same
order as those which may be expected from measuring errors.
Higher precision might be obtained by varying the distance of the
white surface more carefully. In the meantime it has appeared from
a mathematical treatment (not yet published) by WoUDA of the type
vacuum bolometer mentioned, that the linear connection between
incident energy and deflection is guaranteed up to 1 o/q^ so long as
the incident energy does not exceed 5 X 10—4 Watt/cm2. In carrying
out our measurements we took proper care to keep the deviations
from direct proportionality down to 0.2 at the most.

The pyrometer principle of Holborn-Kurlbauiw is the basis on
which the spectral pyrometer is constructed (7). An image of the
object, whose brightness is to be measured, is thrown on the filament
of a pyrometer lamp ; equal brightness of the image and the filament
is then obtained by varying the strength of the current. In order
to compare the image and the filament monochromatically the
filament is placed in front of the front-slit of a monochromator.
Looking into the back slit the filament and the image are seen in
monochromatic light. The apparatus is shown schematically in

fig. 19. As spectral apparatus we used a Hilger spectroscope,
provided with two slits. The slit-height was chosen in such a way
that the troublesome diffraction and reflection phenomena which

occur just whenever the brightness of the filament is almost equal
to that of the background and which, therefore considerably interfere
with the precision of the measurements are entirely absent (8, 9).

To investigate the influence of scattered hght we measured the
brightness of a white surface of constant brightness, of which we
varied the extent of the reflecting area by means of a diaphragm.
From these measurements we found between the results for a small
and a large area, differences of 1 % to 2 %, which must be ascribed
to scattering. The amount of scattered light on the spot where the

image of the pyrometer filament is formed
will be nearly proportional to the size of
the object. It is, therefore, very necessary
when using a spectral pyrometer to employ
for brightness measurements objects of
the same size as for standardizing. A
second effect of scattering consists in
the fact that the light emerging from
the back-slit contains also wave-lengths
20.nbsp;differing from those determined by

sht-width and dispersion ; this is a source of errors whenever
the spectral distribution of the pyrometer lamp and of the object,
to be tested by the pyrometer, differ largely. The amount of this
stray light is nearly proportional to the illuminated area of the
back lens of the spectroscope. To eliminate its influence we placed
a rectangular diaphragm D, of the same size as the image of the
white surface W in fig. 1.

In order to measure the power of reflection of the bolometer-strip
the standardizing was accomplished with the aid of a band lamp
of which at various wave-lengths the energy is known as a function
of the current strength. The bandlamp radiated on to a white
surface of which the brightness was altered in known ratios by
varying the current strength. We measured the strength of the
electric current of the pyrometer lamp, which made the filament
disappear at known brightness of the white surface. This method

of standardizing is, however, too inaccurate for the comparison of
the spectral energy of the band lamp to be standardized, with the
images of which the energy is known; we proceeded, therefore, as
follows:

A sector diaphragm was placed in front of lens Z-g with its centre
on the optical axis of the lens. This contrivance for reducing the
hght has the advantage, that the reduction is the same for every
wave-length and that, moreover, the amount of the reduction can
be very precisely measured in the region of the longer wave-lengths
The error in the reduction over a range from 80 % to 10 % is
smaller than 0.5 %. To eliminate errors which might possibly arise
from differences between the optical behaviour of the various
sectors of the lens, the diaphragm was made to revolve rapidly.

The spectral pyrometer was standardized with the aid of sector
diaphragms; as hght source we used a tungsten band lamp of
which the light corresponds to a colour temperature of 2800° K and
which was placed in P (fig. 1). The measurements were carrfed
out for various wave-lengths lying between 6800 A and 4800 A and
with intensities varying from 1 to 10. In this way a set of curves
with the wave-length as parameter was found which represent the
intensity as a function of the pyrometer current. The largest
deviation of the points actually observed from the smooth curve
drawn through them is 1 %. Each measurement of brightness is
the mean of 3 observations. We measured the strength of the
pyrometer current in compensation connection.

When the brightness of the filament of the pyrometer lamp is
adjusted so as to be equal to that of the background we get the
equation:

Eu. denotes the brightness of the background,
Epx ,, „nbsp;„ „ „ filament.

Ox gt;' quot; sensitivity factor of the eye,
Dx lt;gt; quot; transmission of the spectral pyrometer,

,, „ central wave-length of the region let through,
2a ..nbsp;wave-length region let through, i)

When Elx changes in a similar way as Epx with the wave-length
in the region from (Aq — a) to (.^q s), one can infer from this
equation that Elx^ = Epx„- When, however, the energy distribution
Elx differs from Epx over the range 2a one might compute the
correction to be apphed to the equation En^ — Epx„- Usually,
however, one computes in the case of pyrometric measurements the
so-called effective wave-length, . The simplest way of defining
the latter is by the mathematical equation:

When the energy distributions of the object to be investigated
by the pyrometer, and of the filament, can be described with the
temperatures Tl and Tp one can write for (1), as an elementary
but rather lengthy computation would show:

1) For those wave-length regions under consideration (max. 100 A) the
transmission as function of the wave-length may be taken to be represented by
the two sides of an isosceles triangle.

We computed Xg—lg for those cases in which, when adjusted
for equal brightness, the object to be measured and the filament
had the colour temperatures 2800° K and 1200° K, 2800° K and
1400° K, 2000° K and 1200° K and 2000° K and 1400° K respec-
tively, while the wave-length region let through was 200 A. With
the aid of the table given below we can then easily compute 4—^
for the various other cases,

We shall now discuss, in a short survey, the various factors on
which the precision of a relative energy measurement depends.
Errors in the results of such measurements of a tungsten band
lamp arise from two sources :

2.nbsp;Errors in the comparison of the intensities of the lamp to be
standardized with those of the images.

1. The energy per Ä is computed from the measured transmitted
energy and the wave-length region let through (See § 5).

Now, systematical errors can arise in energy measurements from
a variety of causes, as, for instance, because the bolometer reading
is not proportional to the incident energy. The energies actually
measured lie within an intensity range for which the maximum
deviation from direct proportionality amounts to 0.2 o/qq. The
energy of the auxiliary lamp Q of fig. 1 is sufficient to enable one
to measure the energy of the images in the region from 6800 Ä to
4800 Ä with a mean error in a single observation of 0.5 o/qq- In this
connection we may remark that the relative energy measuring is
reduced to the measuring of an electromotive force supplied by a
voltage source and a precision rheostat (see fig. 2) i).

In addition to the error just mentioned, of 0.5 o/^q, a systematic
error, for which a safe estimate is 0.1 o/q^ can arise from errors in
the resistances of the rheostat.

To form an opinion concerning the precision of measuring for
smaller wavelengths, we registered the deflections of the relay
galvanometer while the monochromator was adjusted on 4200 Ä
and the effective wave-length region was 100 Ä. This deflection
was 3 cm with a mean error of one single observation of 5 o/qq.
The selectivity of the absorption of the bolometer is determined
(see § 7 sub. 3) in the region from 6800 A to 4800 Ä with a precisio
of 0.5 o/oo- By the photo-electric method this determination can be
extended to 4000 Ä with the same precision.

The measuring of the transmission curve belonging to a given
monochromator adjustment was accomphshed to the method
explained in § 4. The precision is influenced by the occurrence of
a weak wing on the monochromatic rectangular images in the
spectroscope (§ 7 sub. 2), To investigate whether the wing gives
rise to systematic errors in the adjustment, the transmission curves
belonging to various wave-length adjustments were measured by
two observers. It appeared then that systematic errors did not
occur; the highest difference between the measurements of the

As a source for the E. M. F. we used an accumulator, checked as to its
constancy by means of a normal element. All precision rheostats are manufactured
by O. Wolff.

two observers in the effective wave-length region (200 A) amounted
to 2 o/oo* The amount found for the energy when influenced by
the wing is at the most 0.1 o/oo too high (see § 7 sub. 3).

The resulting error in the determination of the energy per A of
the images is, therefore, composed of the following factors :

The errors under a. and b. are of a fortuitous character; it is,
therefore, possible to attain a higher precision by increasing the
number of observations. The errors sub c. d. e. and f. are syste-
matic ; their combined influence is smaller than 1 o/qq.

2. The spectral intensity comparison of the lamp to be standard-
ized with the image of which the energy is known was carried out
with a spectral pyrometer in the region from 6800 A to 4800 A. The
precision of the mean of three measurements amounts in this case
to 5 o/oo- As described in § 6 the photo-electric method can be
applied in the region from 6800 A to 4000 A ; the precision is then
1 o/qq. For the intensity comparison we have thus an objective and
sufficiently precise method at our disposal.

When comparing the energy of the lamp to be standardized with
the images for various wave-lengths, the degree of weakening
suffered by the radiation of the images and by that of the lamp
to be standardized, on the way from P to the receiver behind the
spectral apparatus, must be the same. The contrivance of the white
surface eliminates the influence of difference in the filling of the
spectral apparatus and that of the degree of polarisation of the
hght from the images P (see § 1). The tungsten band lamp to be
standardized is put in its right place by the aid of a telescope
directed slantingly on to the light path (see § 2). The error in the
position of the band is at most 0.05 mm, and this influences the
brightness of the white surface. A computation showed us that an
error of 0.05 mm in the position of the band gives rise to an error
in the brightness at the centre of the image on the white plane.

amounting to 0.5 o/qq ^ its influence on the changes in the bright-
nesses as function of the wave-length is smaller.

We have, we believe, shown by the above that a relative energy
measurement of the tungsten band lamp with a precision of 1 %o
is possible. For a detailed discussion of the measuring results we
refer the reader to the next chapter, where we give the measurement
of the spectral energy distribution of a black body at the melting
temperature of gold.

The investigation, carried out with a view to testing the law of
radiation and to determining the constants, occurring in that law,
are very numerous. On a close examination of the work of many
investigators in this field, one can not help doubting, whether the
values, actually obtained, are entirely free from systematic errors.
Indeed, considering.the variety of such errors to which this kind of
work is liable, the agreement between the values, found by the
various writers, is a matter of some surprise !

In table 4 we give a list of values of c^ together with the names
of those, who obtained them i). From a comparison of these values
with the one, adopted by the 7th ,,Conférence générale des Poids
et Mesuresquot; (c2= 1.432 cm degree) the impression will most
probably result that the choice of the latter value is more or less an
arbitrary one.

The investigators, mentioned in table 4, obtained their values for
C2 from intensity measurements on the radiation of a black body,
of which the temperature was determined by means of the gas
thermometer. C2 was then computed, either from the energy ratio
of the radiation, for one and the same wave-length at two different
temperatures, (the isochromatic method) or the wave-length A„„ for
which, at one and the same temperature, the radiated energy was
a maximum, was computed from the change of the energy per A
(the isothermal method) according to the first method C2 is given
by the formula :

We confine ourselves here to the simple statement of the prin-
ciples, underlying the methods which were used, it is not our aim
to criticise the values, so obtained, or to discuss once more, the
many sources of error, which, doubtlessly, have influenced the
results of these investigations. For such a discussion we refer the
reader to the original pubhcations, to the handbooks and to a very
comprehensive article by Coblentz (10).

measured energy-distribution in the spectral region from 0.68 fj. to
0.50 ju, of the radiation of a black body at the melting temperature
of gold. For the quantitative description of this energy distribution,
we used, instead of Planck's law, wlens well-known formula:

That Wien's expression yields in our case a very good approxi-
mation, is clear from the following : denoting the energy, at the
wave-length 2, radiated according to Planck's- and to Wien's
formula by Ep and Ewgt; respectively, their ratio is given by:

moreover, the melting point of gold is known from measurements
with the gasthermometer, we find in this way the value of C2.

However, a new determination of C2 will only be of any use
if the method used, enables one to reach a higher accuracy than
the methods hitherto used.

Now, in order to form an opinion of the accuracy attainable, let
us compute C2 from the ratio between the energies, radiated at
and which is given by:

This means, that an error of 1 % in the determination of the
energy ratio, will cause an error of 0,003 (A, degrees) in the value
for 02-

It will be clear from these considerations, that thanks to the
method of measuring energy ratios, explained in Chapter 1, we
are indeed in a position to determine the value of C2 to a very
high degree of precision.

• The energy distribution in the radiation of a black body at the
melting point of gold was measured with the aid of a primarily
standardized hght source, viz. the images in P (fig. 21). Now, the
obvious way to proceed in measuring the black body radiation in

question would seem to place the body in P, as was done also in
standardizing the tungsten band lamp, and then to carry out the
comparison of the energy distribution by means of a spectral
apparatus Sp (fig. 21). In the present case, however, this procedure
would lead us into unsurmountable difficulties. Indeed, the bright-
nesses of the light sources to be compared, are now so widely

different (in yellow e.q. they differ by a factor of about 1000), that
the brightness of the images in P can no longer be put in line with
the brightness of the black body at the melting-point of gold, by
simply weakening sufficiently the strength of the current in the
auxiliary lamp Q (fig. 21), for in this way it would no longer be
possible to measure the energy of the images at P with the required
precision.

We succeeded, however, in reducing the brightness of the images
m P to a sufficient extent, to make it comparable with the brightness
of the blackbody at the melting point of gold, and we were at the
same time able accurately to take into account the change of the
spectral energy distribution in the images, due to the method of
reduction, by the following contrivances. In the first place, a
diffusely reflecting white surface, with a known reflective power
was placed in P. The images on this surface serve as a primarily
standardized light source; in the red region of the spectrum the
brightness of the images is now about the same as that of the
black body. It was, in the second place necessary as a further
contrivance, to use in the green region a smoked glass reducer, with
a transmission power of about 20 %, which was applied in front
of the monochromator. The brightness of the images on the white
surface was measured for various wave-lengths, with the aid of a
spectral pyrometer by altering the brightness in known ratios by
means of standardized sector reducers. In this way the connection
between the pyrometer current and the relative brightness was
obtained. The pyrometer current belonging to the brightness of the
black body at the melting point of gold, was then also measured,
so that the relative brightness of the black body was found as a
function of the wave-length from the established connection, just
mentioned. From this we obtain finally the value of cg, in the
manner, described in § 1.

Apart from serving as a reducer, the white surface is an essential
feature in our arrangement in another respect as well; for its
diffuse reflection and depolarising action bring about, that the
hght, radiated on to the spectral apparatus either by the images or
by the black body is ordinary hght, which, moreover, travels, in both
cases, along identical paths through the apparatus (c.f. Chapter I
§ 1).

The spectral pyrometer is mounted vertically so that the image
on the white surface and the wire are observed in the instrument as
is indicated in fig. 22a, whereas they show as in fig. 22b, when the

It follows from the above, that apart
from the measuring of the spectral energy
distribution in the images in P, it is
quot;nbsp;Fig 22 ^nbsp;necessary to carry out the following

1.nbsp;of the pyrometer current, on adjusting for a brightness, equal
to that of the black body at the melting temperature of gold.

2.nbsp;of the reflective power of the white surface, and of the
transmission curve of the smoked glass.

The method of determining the spectral energy distribution in
the images was already explained in detail in Chapter I, as was
also the spectral pyrometer. We shall, therefore, now proceed
to give particulars of the black body used by us, and the complete
series of measurements, which have served to obtain the value
for C2.

Our black body consisted of nickel and was of the Lummer and
KurLBAUM type. It was heated in an electric Heraeus furnace,
(length 30 cm, aperture 6,5 cm).

In order to obtain an even temperature throughout the furnace,
the heating platinum band was wound closer together in the centre
than at the ends. The way, in which the black body is mounted in
the furnace is shown schematically in fig. 23.

For the determination of the temperature of the black body, at
the melting point of gold we used the so-called „wire methodquot;,
according to this method a thermo-element (Pt, Pt~Rh), fitted with

1) Since, for the sake of accuracy, the pyrometer wire and the slit of the
spectral instrument must be at right angles to each other ; a horizontal position
of the spectral pyrometer (i.e. slits of the monochromator vertical and pyrometer
wire vertical) is in our case excluded. Of these two positions the former allows
of the better adjustment.

a gold 1) wire between the Pt, and Pt~Rh wires (see Au in fig 23),
is inserted in the interior of the black body. There is still another
thermoelement, inserted in it, which, however, is not shown in
the figure.

With the aid of an electrical connecting-system, as shown in
fig. 24, the E. M. F., of the two elements are measured, with the
temperature slowly increasing, as a function of the time. One
notices the moment, at which the temperature in the furnace has

reached the melting point of gold, by the fact that, from then
onwards, the E. M. F. of the gold-wire thermoelement remains

The gold, used in our experiments, was supplied by the Royal Dutch Mint,
at Utrecht. Our sincere thanks are due to the mint-master Dr. v. heteren
for his courteous help in this matter.

constant for a few minutes, where upon the circuit is suddenly
interrupted by the melting of that wire^) whereas in the meantime
the E. M. F. of the second element continues to increase slowly
(see fig. 25).

the melting temperature of gold, serves for heating the black body
to that temperature again later on.

In order to make the actual radiation comply with the definition
of black radiation, the radiating body must satisfy two conditions,
viz , its coefficient of absorption must be equal to 1, and the walls
of the enclosure must possess the same temperature throughout.
As regards the first condition, the observation may suffice here,
that part of the radiation, incident in the enclosure, may eventually
find its way out of it, in which case the absorption coefficient would

1) The actual interruption of the circuit takes place at a higher temperature
of the furnace. The latter is at the melting point of gold, at the moment, the
constancy of the E. M. F. sets in; this means that the temperature of the black-
body, yielded by the method of melting a gold wire is too low.

differ from 1. As for the second condition, there are two causes,
from which an uneven distribution of the temperature over the
walls can arise. There is. first, a wrong way of heating, and, con-
sequently a temperature gradient in the length direction of the
black body, and there is, secondly, the fact, that the part of the
black wall, radiating outwards through the diaphragms, will be
at a lower temperature, owing to the fact that the radiation, emitted
by that part, must be completed again by radiation and conduction
from parts of the wall at a higher temperature. To form an opinion
of the temperature gradient along the black body, we may remark,
that with a heating velocity of 0,1° to 0,2° pro minute, the eye
can no longer distinguish the diaphragms from the rear wall. Now,
the eye is able to notice a difference of 1°, at the melting-point
of gold ; it is, therefore, quite safe to assume that the drop in the
temperature over the whole length (6 cm) is less than 1°.

Various investigators have computed an upper limit for the
deviation of the radiation in an enclosure from the theoretically
defined black radiation, so e.g. Fleury in his quot;Etalons Photo-
métriquesquot; and Ribaud in his quot;Pyrométrie Optiquequot;. On applying
these considerations to our case, it follows that the deviation from
the theoretically black radiation in the visible region of the spec-
trum, amounts at the most to 0,1 %. The deviations in our spectral
energy distribution, are therefore, certainly less than 0.1 %.

As explained already in § 2, we must know the spectral energy
distribution in the images in P. Now, in our experiments, this
surface (magnesium oxide) is placed in P at right angles to the hght
path, and the brightness of the images is measured by means of a
spectral pyrometer, of which the optical axis makes an angle of
about 20°, with the light path behind the monochromator. It is
therefore, necessary to measure the selectivity of the reflective
power of the surface under the same conditions i.e. for hght,
incident at right angles and reflected at an angle of 20°. This
was done in two steps. First, the reflective power was measured,

according to the method of Hamaker (6) as a function of the
wave-length, in the case of perpendicular incidence. This gives the
ratio between the total amount of the reflected light and the incident
hght.

Secondly, we measured, for various wave-lengths the brightness
of the white surface as a function of the angle of reflection, from
which it appeared that, in the visible part of the spectrum at least
the connection between the brightness and the angle of reflection,
was not influenced by the wave-length i).

These twofold measurements teach us, that, with perpendicular
incidence, the reflective power, in the case of an angle of reflection
of 20°, is proportional to the numbers measured, according to the
method of Hamaker.

In § 2, we mentioned already the essential part, played by our
white surface owing to its depolarising action. Now, in our arran-
gement, the vibrations of the polarised light, which has travelled
through the double monochromator, are at right angles to the
vibrations of the light, which has passed through the monochro-
mator of the spectral pyrometer. One may expect, therefore, that,
if the degree of polarisation of the former vibrations should depend
on the wave-length, a non complete depolarisation by reflection on
the white surface, would be a source of errors. In order to make

the aid of the arrangement,
shown in fig. 26, the bright-
ness, for various positions
of the nicol N, of the image
of a tungsten band lamp Q,
on the white surface W.vl.
The brightness appeared, for the various wave-lengths, to be
independent of the position of the nicol, from which we can infer.

1) One can not dispense with the measuring of the brightness as a function
of the angle, because it is by no means self-evident, that the relation between
the reflective power and the angle of reflection, is independent of the wave-length.
If a dependence should exist, the functional relation between the reflective power
and the wave-length in the case of perpendicular incidence and reflection at an
angle of 20°, would be different from that relation in the case of perpendicular
incidence and the total amount of reflected light.

that a non complete depolarisation caused by the reflection on the
white surface does not occur.

In measuring the transmission curve of this reducer, the com-
plication arises, that the arrangement used in measuring the energy
of the images in P, in which the bolometer-strip is perpendicular

bolometer
strip

p	1	q
	1

results. The bolometer-strip
was, therefore, placed parallel
to that direction (fig. 27b).

smoked glass reducer serves to
weaken the brightness, in the green region of the spectrum, of the
images on the white surface, sufficiently to make a direct comparison
possible with the brightness of the black body, at the melting point
of gold. Now, when the reducer is inserted in the lightpath, the
brightness of the images is computed from the measured energy,
and the transmission of the smoked glass. In doing so, however,
one must not overlook the fact, that in measuring the energy, the
relative position of bolometer-strip and image, is as shown in fig. 27a,
whereas, when the transmission is measured, it is as shown in
fig. 27b. Now, it will be clear, that in our case, we must know in
particular the transmission of the smoked glass, corresponding to
that part (viz. pq) of the image, which radiates on to the bolometer-
strip in the orientation of fig. 27a, and one must admit the possi-
bility, that the transmission of the smoked glass corresponding to
the various parts of the image, is different from the transmission,
corresponding to its central part (p, q), for the paths of the light-
rays, belonging to the various points of the image, are different.
In order to make sure about this, we measured the transmission
for various heights of the slit, using red light, since the accuracy
of measuring attainable, with this part of the spectrum, is amply
sufficient. It appeared, as a result from these measurings, that a
systematic change of the transmission with the height of the slit,
was absent.

As an instrumental detail, we mention here, that the reducer is
fitted with a revolving and arresting arrangement, so that it can
be inserted in the lightrays, in front of the double monochromator,
in a position, which is reproducible at will.

These reducers, placed in front of lens Lo fig. 22. serve to vary
the brightness of the images in P over a range, which includes the
brightness of the black body at the melting point of gold. The use
of these sector reducers has the important advantage, that the
transmission is independent of the wave-length. It is, therefore,
possible to measure the transmission with red light, which allows
of a high precision. During the measuring, bolometer-strip and image,
are at right angles to each other. It appeared to be necessary to
mount the stand and holder of the reducers in such a way that the
mechanical vibrations, arising from the rapid rotation, can not have
a disturbing influence on the bolometer-strip. When for example,
the stand, which carried the reducers, was fastened on to the same
table, on which the bolometer was placed, the zero of the relay
galvanometer showed rapid unsystematic fluctuations of about 3 mm.
These fluctuations, which made an accurate determination of the
transmission impossible, must be ascribed to the induced vibrations
of the bolometer-strip.

The construction of the stand and of the revolving holder was
such as to prevent an arrangement, which would make the position
of the sector reducers in the path of the light reproducible at will.
It was, therefore, necessary, contrary to the adjustment of the
smoked glass reducer, to measure the transmission of the sector
reducers anew, each time they were inserted in the light path.

10. The measurings of the current running the pyrometerlamp,
when the latter is adjusted for a brightness, equal to that of the
black body at the melting temperature of gold.

1°. In order to determine the pyrometer current corresponding
to the brightness of the black body, at the melting temperature of
gold, we proceeded as follows :

While the temperature was made to increase at the rate of 0,1°
per minute, the pyrometer current was determined, for the various
wave-lengths, as a function of the heating time, as were also the
E. M. F.'s of the two thermoelements. Now, at the moment, the
constancy of the E. M. F. of the gold wire element sets in, the
black body has reached the melting temperature of gold; the pyro-
meter current in question, is therefore found for the various wave-
lengths from the known connection pyrometer current-time by
interpolating to that moment.

Table 5 gives for the various wave-lengths the pyrometer currents
corresponding to the brightnesses of the black bodyi).

As regards sub. 2, the condition must be satisfied that the bright-
ness of the auxiliary lamp Q remains constant during the relative
standardizing of the spectral pyrometer. In order to obtain a
constant energy radiation, the current was, therefore, adjusted for
unvarying strength bij means of a compensating arrangement, which
made it possible to reach an accuracy of 0.1 o/qq in the constancy 2).
However, since the constancy of the current is not a sufficient
guarantee for the constancy of the radiated energy, it was still
necessary to check the latter during the relative standardizing of the
spectral pyrometer. As already mentioned in § 4, the sector reducers
could not be inserted in the lightpath in a reproducible position, and
their transmission must, therefore, be measured each time a new.

We observed, in a few cases that the E. M. F. did not remain constant
during the melting, but showed a slight decrease.

2) A fluctuation of 0,1 quot;/oo in the current means a change of 0,3 quot;/oo in the
radiated energy for the type of lamp, used in our case.

It follows from the above, that the bolometer-strip and the white
surface must alternately be put in P (fig. 21) in a reproducible
way. In order to make this possible the bolometer and the white
surface are each mounted on a stand, of which the legs end in sharp
points, resting on three metal blocks. Of the latter, one is plane,
one has a groove in it, and the remaining one has a hole in it. The
three blocks are fastened on to the same iron plate, which carries
the whole of the arrangement.

The adjustment of the white surface and of the bolometer is
then effected as follows :

The white surface is placed in P, in such a way, that the images
on it, are sharp, and its position fixed by means of a telescope
provided with cross threads, which is put, as nearly as possible, at
right angles to the lightpath behind the monochromator. The
bolometer-strip is then, in its turn, adjusted with the aid of the
telescope. The stands, which carry them, make small displacements
in three mutually perpendicular directions possible. Each time, the
bolometer-strip and the white surface were inserted in the light path,
their positions were checked by the telescope, and the experiments
proved that this way of proceeding was indeed successful for
obtaining reproducible adjustments.

In order to eliminate errors, arising from slight changes in the
arrangement which preliminary experiments had shown actually to
occur, we tried to obtain the values for the required quantities from
observations, which were, as nearly as possible, simultaneous.

We shall now give the complete set of measurings, to be carried
out, which is involved in our method of proceeding :

§ 4, and of the bolometer-strip, Ch. I, § 7.
20. of the transmission of the smoked glass reducers, § 4, and
of the bolometer window (bolometer-strip parallel to the length
direction of the images).
30. of the wave-length regions, let through by the spectral pyro-
meter, § 4, and besides, measurings for the determination of
the connection, wave-length-reading — true wave-length.
40. of the regions, let through by the double monochromator, Ch. I.
§4.

50. of the energy of the images, Ch. I, § 3 ; measurings from which
to deduce the connection brightness-pyrometer current, § 3, and
the measuring of the transmission of the sector reducers, § 4.
(bolometer-strip at right angles to the length-direction of the
images).

60. the checking of the measurings sub. 4, by repeating them.
70. the checking in the same way of no. 3.
80. the checking in the same way of no. 2.
90. the checking in the same way of no. 1.

A few points ask for more elucidation. For the determination of
the transmission of the bolometer window, a glass plate was used,
cut from the same plate as the window itself.

The measuring of the wave-length-regions, let through by the
spectral pyrometer, is required for the determination of the effective
wave-length ; a high accuracy is not necessary in this case.

As regards the check measurings sub. 6 and 7 preliminary experi-
ments showed them to be absolutely necessary; it has actually
occurred, for example, that the adjustment of the slits had for some
unknown reason, suddenly changed by which, of course, the
regions, let through, as well as the energy of the images, were
also altered.

The measurings sub. 5 require an alternate determination of the
energy and the brightness of the images in P; the order of the
necessary manipulations is here chosen in such a way as to make
their number a minimum.

In table 6 we give the measurements referring to the measuring
programme mentioned sub. 5. The measuring ot the energy of the
images is carried out for wave-lengths, lying close to those for
which the brightness was measured.

The transmission of the sector reducers was measured in the red
region, the reading of the wave-length adjustment being 14.70.

By the arrangement of the measuring programme as given above,
we are in a position to check the constancy of the radiated energy,
during the relative standardizing of the spectral pyrometer, and
to measure the transmission of the sector reducers, when inserted
in the light parth.

The resuhs obtained from a series of measurings which served
to deduce the value of Cg are collected in table 7. The measurements,
from which the relative brightness of the images per a was com-
puted, are given in the last column.

The relative brightness per A of the images is determined as the
quotient of the energy obtained and the effective wave-length-
region. As already explained, however, in Ch. I, § 5, a correction
must be applied to the value, so computed, owing to the change
of the energy with the wave-length in the auxiliary lamp. Besides,
there is still another correction required, due to the fact, that the
shape of the area, covered by the transmission as an ordinate over
the wave-length-region, let through, differs slightly from a trape-
zium. These corrections were computed from the approximate values

of the relation energy pro A, given in column 5 of table 7. The
latter was computed according to the formula:

where A denotes the measured energy of the image, A/l the
corresponding effective wave-length-region andnbsp;the energy

per A, belonging to Xq —, i.e. the wave-length corresponding to
the apex of the triangle (point B. fig. 10) when the transmission

area has a triangular shape, and to the centre of the shorter parallel
side, when it has the shape of a trapezium.

The correction factor [ was determined for the various wave-
lengths by means of a graphical solution of the equation :

where Ex denotes the approximate value for the energy per A,
given in Column 5 of table 7.

Since we have to deal, in our case, with relative energy
measurements, the maximum error, which can arise from neglecting
this correction, amounts to 0,4 o/qq.

Each time a sector reducer was inserted in the lightpath, the
energy was measured anew, for which the red part of the spectrum
was used (with the wave-length reading of the double mono-
chromator at 14.70). The values, so obtained, which give an account
of the behaviour of the energy radiated during the standardizing
of the spectral pyrometer, are collected in table 9.

Table 10 gives the values, found for the transmission of the
various sector reducers.

For the comparison with the brightness of the black body, at the
melting point of gold, the brightness of the images was measured
over a range, which, was reduced so as to include the former
brightness, by the use of the smoked glass- and sector reducers.
In table 11 are given the pyrometer currents, measured for this
comparison.

From the connection pyrometer current-transmission of sector
reducers, found in measuring the brightness of the images, we
obtained, by interpolating to the pyrometer current, belonging to
the brightness of the black body at the melting point of gold, the
reduction factor r. (last column of table 11), which must be applied in
order to make the brightness of the images on the white surface
equal to that of the black body.

In this way, therefore, we arrive at a brightness of the images,
as observed in the spectral pyrometer, which is equal to that of the
black body at the melting point of gold, likewise observed in the
spectral pyrometer. This equality is expressed mathematically by:

Here, A' and Iquot; denote the limits of the spectral region, let through
by the spectral pyrometer,

Dx the transmission of the spectral pyrometer,
Ox the sensitivity-factor of the eye.

*) For these measurements, the smoked glass and the sector reducers were together inserted, at the same time in the Hght path.

In Ch. I, § 7, we explained already how from this equation the
brightness per A of the black body is computed at the effective
wave-length; the latter being defined as that particular wave-length,
for which the energies per A of the images and of the black body
are equal.

We obtained the effective wave-length from the data of table 3
and the measured spectral region, let through by the spectral
pyrometer. The results are given in table 12.

For the relative brightness per A of the black body at the
melting point of gold, we have the expression:

where Ez). denotes the brightness per A of the black body.
Ex denotes the brightness per A of the images,
r the reduction factor given in table 11,
dx the transmission of the smoked glass,
wx the reflection coefficient of the white surface,
bx the transmission of the bolometer window.

The values for these quantities are collected in table 13, where
one finds besides in column 7 and 8 the values for — and for
log. Ej^^ P respectively.

As a final result from our measurements, we can therefore take
C2 to be the mean of these two values, i.e.

As already explained in § 1, an error of 0,003 in the value for c^
from an error of 1 % in the value for the measured energy ratio,
and in connection with what was said of the high accuracy of
the relative energy measuring, one would probably expect a closer
agreement between our two separate results for C2. The explanation
of this discrepancy, however, is, that one must distinguish, in our
case, between the method as such, and the apparatus, at our
disposal. As regards the latter, it is more in particular the reliability
of the double monochromator, in its present construction, which
falls decidedly short of what is required of it.

Russell vervangt in zijn berekeningen de werkelijke ster-
atmosfeer door het model van schuster-schwarzschild, daarbij
de „effectieve dieptequot; van de fotosfeer constant aannemend. Hier-
door kunnen aanzienlijke fouten ontstaan.

Een betere en meer economische wegverlichting is te verkrijgen,
indien de bouw van de lantaarns aan de reflectie-eigenschappen
van het wegdek aangepast wordt.

Alvorens de monochromatische wegverhchting algemeen toe te
passen, behoort o.a. onderzocht te worden, of de mérites van ge-
noemde wegverlichting ook voor kleurenblinden gelden.

Voor de vraagstukken van dag- en avondverlichting is een
systematische studie der lichtverstrooiende en lichtrichtende mate-
rialen noodzakelijk.

De gevoeligheid van spectraal fotometrische meetmethodes
volgens het beginsel der gelijktijdige waarneming, is kleiner dan
van de methodes volgens het beginsel van successieve waarneming.

Het is gebruikelijk de temperatuurschaal aan de smeltpunten van
verschillende stoffen vast te leggen ; als zoodanige stof is Palladium
niet geschikt.

_______					...S2.....5
				. -- -	'2.....
-9i-	.....	-	--	-92--	— y
R-fl			T	X	rt
					P -a.

Wave-length	Colour temperature 2800° K
Wave-length	e}
4000 A	20.5X 10-^	1.27 XlO-6
4500 .,	14.2X10-4	0.56 XlO-6
5000	10.5 X 10-4	0.23 XlO-6
5500 „	7.8X 10-4	0.08 XlO-6
6000 „	5.9X 10-4	0.007 X 10-6
6500 „	4.4X10-4	-0.03 XlO-6
7000 „	3.2X 10-4	-0.046 X 10-6

Angle	fW)	iwM
10°	0.0530	100
20	0.0377	100
30	0.0270	99,4
40	0.0225	97.2
SO	0.0195	93.2
60	0.0165	86.8
70	0.0145	74.3

}.o	2800° K-1200°K	2800^ K-1400°K 1	2000° K-1200° K	2000° K-1400°K
0	o	O	0	0
6800 A	-10.2A	10.4 A	— 9.8A	- 9.9A
6600	- 7.3	- 7.5
6400	— 4.6	- 5.2	- 4.4	- 4.6
6200	— 3	- 3.2
6000	- 1.2	— 1.5	- 0.6	- 0.9
5800	2	3
5600	2.4	1.9	2.9	2.4
5400	4.3	4.3
5200	4- 7.4	7.4	8.2	7.4
5000	10.2	10.2
4800	11.5	11.5	11.5	11.5

Observer	Date	Xml observed	1 ImT corrected	c2	c2 , probable value in micron deg.
Paschen	1899	2891	2891		14360
		2907	2907
LuMMER and	1900	2921	2894
Pringsheim	1900	2879	2879	14290
		2876	2876
		2940	2882	H310	14300
Warburg and	1911			14200—14600
Collaborators	1912			14300-14400
	1912			14360
	1913			14370
	1915			14250
	1915			14300-14400	14300
Coblentz	1913	2911		14456
	1916	2894		14369
	1920			14311-14318	14318

Wave-length reading of the double monochromator	Resistance in W2
19.90	38000 lt;i — 36000 .lt;2 (steps 500 S)
20.00	38000 a - 36000 lt;2 (steps 500 ii)
14.70	7500 a-7300 .lt;2 (steps 50 .lt;2)
Sector reducers in light path, measuring of the transmission
14.70	8600 .lt;2 — 8400 J2 (steps 50 a)
Brightness measuring, with sector 1 in light path
Wave-length reading sp. pyr.	Pyrometer current in m. Amp.
6060	26635
6140	26275
6230	2605

5380			25965
5200			26295
5110			2655
Sector 1, replaced by 5
5110			25825
5020			26135
5200			25575

5720	26885
5890	26275
6060	25715
Energy measuring, sector 5 in the light path
Wave-length reading double mon.	Resistance
H.70	13400 ii — 12800 a (steps 200 a)
Sector reducer out of light path
H.70	7500 ii — 7300 2 (steps 50 a)
Energy measuring of the images
1520	8600 ii - 8400 a (steps 50 a)
___

Wave-length reading double monochromator		Effect, wave-length- region	Energy image	Rel. brightn. pro A
14.70	6590 A	330.2A	13452	203.5
14.90	6511.5	318.3	12722	199.8
15.-	6474.0	312.6	12405	198.5
15.15	6418.0	304.1	11865	195.1
15.25	6381.5	298.5	11483	192.4
15.70	6227.0	273.9	9990	182.4
15.80	6194.5	268.7	9738	181.1
16.35	6023.0	241.9	8172	168.9
16.45	5993.5	237.5	7928	166.9
17.00	5842.5	215.7	6713	155.6
17.10	5816.0	212.8	6496	153.2
17.85	5628.5	187.1	5209	139.2
17.95	5606.0	184.3	5044	136.8
18.80	5424.0	162.5	3855	118.5
18.90	5403.5	160.3	3745	116.8
19.35	5316.0	150.7	3249	107.7
19.45	5297.5	148.4	3135	105.3
19.90	5216.5	140.2	2732	97.4
20.00	5199.5	139.4	2653	95 .'8

Adjustment	J	Pyrometer currents in m amp. occurring with the reducers
Sp. Pyr.	e	No	Smoked glass	1	2	3	4	5	6	7	r in O/o
5020	5198.5					2624*	2613.5*	2571*	2573*		43.7*
5110	5301.5			2655'	2621.5*	2593.5*	2582.5*	2539*			56.0*
5200	5404.5			2629.5*	2596.5*	2571.5*	2557.5*				68.2*
5380	5610.5		2618	2596.5*	2557*						85.0*
5550	5805		2545.5						2683.5	2618	25.7
5720	6004.5						2688.5		2623.5	2563	35.6
5890	6206.5					2638	2627.5	2574	2567.5	2511	50.0
6060	6406.5			2663.5	2616.5	2584.5	2571.5				68.8
6140	6499.5	2661.5		2627.5	2593.5						78.1
6230	6605	2632		2605	2562						90.4

Wave-length adjustment Sp. pyr.	Wave-length region	gt;•0	Effective wave-length
6230	244 A	6615.5 A	6605. OA
6140		6507.5	6499.5
6060	218	6412.5	6406.5
5890		6209.5	6206.5
5720	180	6005.5	6004.5
5550		5805.0	5805.0
5380	148	5609.0	5610.5
5200		5402.5	5404.5
5110	120	5299,0	5301.5
5020		5196.0	5198.5

Xe		r	dx	quot;A	h	'A.
5198.5A	95.70	43.70/0	18.300/0	9I.8OO/0	92.OOO/0	1.9236xl0-t	2.471
5301.5	105.5	56.0	17.84	91.76	91.94	1.8862	2.644
5404.5	116.8	68.0	18.12	91.71	91.87	1.8502	2.821
5610.5	138.5	85.0	20.52	91.59	91.70	1.7832	3.128
5805.0	152.2	25.7	—	91.46	91.42	1.7227	3.412
6004.5	167.6	35.6	—	91.29	91.18	1.6653	3.669
6206.5	181.6	50.0	-	91.09	90.84	1.6112	3.923
6406.5	194.2	68.8	—	90.88	90.48	1.5609	4.161
6499.5	199.3	78.1	—	90.73	90.30	1.5385	4.259
6605.0	208.0	90.4	—	90.56	90.10	1.5140	4.376

o
;.in A	6800	6200	5600	5000
	1.0006	1.0007	1.0008	1.001